Question: Simplify to lowest terms. $\dfrac{36}{60}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 36 and 60? $36 = 2\cdot2\cdot3\cdot3$ $60 = 2\cdot2\cdot3\cdot5$ $\mbox{GCD}(36, 60) = 2\cdot2\cdot3 = 12$ $\dfrac{36}{60} = \dfrac{3 \cdot 12}{ 5\cdot 12}$ $\hphantom{\dfrac{36}{60}} = \dfrac{3}{5} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{36}{60}} = \dfrac{3}{5} \cdot 1$ $\hphantom{\dfrac{36}{60}} = \dfrac{3}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{36}{60}= \dfrac{2\cdot18}{2\cdot30}= \dfrac{2\cdot 2\cdot9}{2\cdot 2\cdot15}= \dfrac{2\cdot 2\cdot 3\cdot3}{2\cdot 2\cdot 3\cdot5}= \dfrac{3}{5}$